Visualizing differential geometry in Jupyter notebooks
(you can download this post as a notebook here)
Visualizing differential geometry in Jupyter notebooks¶
I taught a senior seminar on differential geometry last year. I'll be honest: it was a selfish course. Markus Deserno writes all of these cool papers about membranes, and I didn't know enough math to follow them. So, the goal of our course was basically to learn enough differential geometry to read several of his papers. It was fantastic. We used several of his papers, as well as Kreyszig's textbook, as our core materials.
Here's the thing: a lot of this was pretty foreign to my physics students. In particular, the discussion of surfaces and mappings was new. So, we wrote some tools in Jupyter Notebooks to help us visualize and solve problems. I particularly like the stuff we wrote to visualize a mapping, and I don't know of a comparable resource elsewhere.
As a teaser, the above movies show you how to interpolate between a surface and a curve in the first case, and how the Monge gauge works for a membrane in the second case.
Let's jump in.
Arindam Paul 
Nils Wagner 
Andreas 
gmas 
X 
mglerner 
Ben 
Your IPyNB class could be made a lot more readable by using a custom JSON encoder, e.g. extending JSONEncoder http://docs.python.org/2/library/json.html#json.JSONEncoder. That way, you could store the preamble/afterward as a Python dict and just call json.dumps(..., default=MyJSONEncoder) inside tostring().
Updated above, after our email conversation.